In fault tree analysis (FTA), and in a case that minimal cut sets are required to have at most a certain maximal order, for example, M, a weeding algorithm is introduced to remove an overlong conjunctions (or combinations) of events generated during evaluation of the MCSs.
A classical weeding algorithm is disclosed in NPL 1. Given a conjunction, and representing the number of order of the conjunction as V, it can be calculated by: V=α+β+δ. in which α and β denote the numbers of the basic events of the conjunction and the disjunctions (OR gates) with only basic events none of which is included in category 1 and no commonality among themselves, respectively. The parameter δ is set to 1 if the conjunction contains a set of disjunctions with only basic events none of which is included in category 1 but contain a commonality among themselves; otherwise, δ is set 0.
In this algorithm, basic events and two types of OR gates are taken into account, and individual numbers of orders of other gates, such as k/n gates, are excluded (that is, the numbers of orders are simply regarded as zero when calculating V).
Moreover, a standard expanding algorithm of k/n gate is disclosed in NPL 2. According to NPL 2, and representing e1, . . . , en as events, a k/n gate as given by:k/n(e1, . . . ,en)can be expanded in the form given by:k/n(e1, . . . ,en)=e1·(k−1)/(n−1)(e2, . . . ,en)+(k)/(n−1)(e2, . . . ,en)The time complexity of this expanding algorithm can be reduced by:O(k·n)as compared with a conventional calculating method.